+2440 A period is the length from one peak to the next immediate peak on a periodic function.
In this particular problem, there is a peak at \(-\frac{3\pi}{4}\) ,and there is a peak at \(\frac{\pi}{4}\). The distance between the two is \(|\frac{-3\pi}{4}-\frac{\pi}{4}|\) or \(\pi \) units.
